Analytical solution for coupled partial differential equations

[jj231]

Hello,

In my study i came across to solve the analytical solution for coupled equation y(x,t) and z(x,t).The equations contains" f " function which is a function of the first variable exponentially.

The first equation is : ∂y/∂t=∂^2(y)/∂x^2- 2*f(y)*z;
The second equation : ∂z/∂t=∂^2(z)/∂x^2-f(y)*z;.

and f is correlated with y exponentially e.g. f=exp(1/y).I have to solve for any type of boundary conditions. I have got a problem in finding the coupled solution. Can anyone please help me to start this problem?

Thanks in advance.

 

[Mute]

It looks like if you multiply the second equation by -2 and add it to the first equation you will get a simpler equation for y - 2z. You can use the result to eliminate, say, z in one of the equations and get a single equation for y.